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Behavior and Properties of Functions

Behavior and Properties of Functions

Assessment

Interactive Video

Mathematics

11th - 12th Grade

Hard

Created by

Thomas White

FREE Resource

This video tutorial covers sinusoidal graphs, focusing on functions that can be modeled by sine or cosine functions. It includes detailed analysis of functions f(x), G(θ), H(θ), and K(θ), explaining how to find their period, frequency, amplitude, and midline. The video also explores the behavior of these functions over different intervals, discussing concepts like concavity and rate of change. The tutorial is part of the AP pre-calculus curriculum, specifically topics 3.4 and 3.5.

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33 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What type of functions can model sinusoidal graphs?

Linear and quadratic

Sine and cosine

Exponential and logarithmic

Polynomial and rational

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the period of the sinusoidal function f(x) if measured from peak to peak?

4

2

3

5

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is the frequency of a sinusoidal function determined?

By adding the period

By taking the reciprocal of the period

By halving the period

By doubling the period

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the midline of the function f(x) if the highest value is 3 and the lowest value is -1?

y = 0

y = 1

y = 3

y = 2

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the amplitude of the function f(x) if the midline is y = 1 and the highest value is 3?

1

2

3

4

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the period of the sinusoidal function G(θ) if it stretches from 0 to π/2?

π/2

π/4

π

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the frequency of the function G(θ) if the period is π/2?

π

2/π

1/π

π/2

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